The scales of commerce and trade: ballancing betwixt the buyer and seller, artificer and manufacture, debitor and creditor, the most general questions, artificiall rules, and usefull conclusions incident to traffique: comprehended in two books. The first states the ponderates to equity and custome, all usuall rules, legall bargains and contracts, in wholesale ot [sic] retaile, with factorage, returnes, and exchanges of forraign coyn, of interest-money, both simple and compounded, with solutions from naturall and artificiall arithmetick. The second book treats of geometricall problems and arithmeticall solutions, in dimensions of lines, superficies and bodies, both solid and concave, viz. land, wainscot, hangings, board, timber, stone, gaging of casks, military propositions, merchants accounts by debitor and creditor; architectonice, or the art of building. / By Thomas Willsford Gent.

PROBLEME VI.

To measure Hangings, Wainscot, Pavements, Land, &c.

The last Theorem is an undoubted speculation to all these, so I will shew the practise of it com∣pendiously with examples; and first, there is a Room to be hang'd, containg of Flemish yards, in height 4 of those measures, and in compasse 25, the product of them is 100. the superficial content; in this room there is a chimney-piece containing 9 ½ square yards, and the Window 10 ½ yards, the summe 20, which deducted from 100 yards, the remainder will be 80 Flemish yards to furnish that room. And as for Wainscot, the operation's the same, but differing in yards, and sometimes by cu∣stome, in takin those measures, as in the height and compasse of the room wainscoted, some using a small line extended straight upon each pannell, and then rising over each stile and quarter. Thus Joyners will make their work both of a greater height and compasse then a line extended over all can do, the reason the workman gives, they must be paid where their Plane goes; but their measures admitted of, finde the su∣perficiall content in the same manner as it was before, yet the Wainscot of that roome, by the same measure, may exceed the other 5 or 6 yards, yet more or lesse according to the Joyners work.

Pavements are usually measured by the foot, or yard square, as Board and Hangings are: the longest lineall measure used in England is the Rod, Pole, or Pearch, whose lengths are various for Land, as custome hath introdu∣ced and continued them in particular Coun∣treys, and those from 15 to 25 feet in length: the most equall and generally received Pearch is 16 ½ feet long commanded by Statute, yet 160 square Pole is one Acre of ground, according to the Rod by which it was measured, and in that Pro∣vince where it is allowed. But as for our pre∣sent purpose, the Survey being taken (though the field be never so irregular) it may be reduced into Triangles, and then measured, as was said before in the first Probleme.

[illustration] diagram

Example.

The Area here surveyed is represented by the fi∣gure A. B. C. D. E. whose superficiall content by naturall Arithmetick will be thus discovered: Draw a straight line from E to C. now A C in this proves a subtendant side to the right angled triangle A.B.C. whereof A.B. was measured by the chain, and found equal to C. D. 45 ½ Perches: from E let fall a Perpendicular on C. D. as E.F. measured with the scale (by which the Plat was ta∣ken) 39 Poles: the work thus prepared, by the first Prob. B. C. 60 2••/33 or 60 2/11 P. multiplied by 45 ½ P. according to the rules of fractions (as in lib. 1. sect. 2. Parag. 4. Parad. 4.) will produce 60692/22 take ½ of it, 'twill be 60697/44 which is 1379 21/44 square Perches. Again, by the first Probleme, in the Tri∣angle E.C.D. the line C.D. 45 ½, or 91/2 Poles, mul∣tiplied by the Perpendicular E.F. 39 P. produceth 3549/2 square Perches, ½ of it is ••549/4 that is 887 ¼ P. the true content of the Triangle C.E.D. the summe of these two Triangles is 2266 ••/11 P. which divided by 160, the square Perches contain∣ed in an Acre, the quotient will be 14 Acres, 0 Rood, and 26 square Pole, the superficial quan∣tity of the Field, as was desired. And thus the Triangle A.E.D. proves 3 A. 12 Pole.

Any Parallelogram or long square propounded, whose dimension is required, multiply the length by the breadth, the product answers your desire: As for example in Decimals, the figure to be mea∣sured is A.B.C.D. in length B.C. or A.D. 60 P.

10 ½ F. in breadth 45 perches 8 feet and 3 inches, what is the Area or superficial content of this ground? 160 square perches makes one Acre, which contains 4 Roods, and one of them 40 Pole; now from the dimension of this field, in the se∣venth table of Decimals look 10 ½ feet, that is 21 half feet, whose Decimal is 6364, to this prefix the integers given as 60 Pole, which number will stand thus, 60.6364. and 45 perches 8 feet and 3 inches, that is ½ a rod, will be 5 for the half pole, so the multiplier is 45.5, the product of these is 2758.95620, which decimal fraction being very near an unite, the integer I make 2759 square per∣ches, which divided by 160 pole, the quotient will be 17 acres and 39 square perches, the Area or su∣perficial measure of the Field required. This Proposition in Decimals is usefull for Survey∣ers.